An analytical synthesis of fractional order PIλDμ controller design. (December 2022) - Chen, Pengchong; Luo, Ying
Abstract: This paper proposed a comprehensive synthesis of fractional order PI λ D μ (FOPI λ D μ ) controller analytical design, which is illustrated through the typical first order plus normalized time delay (FOPNTD) systems, with fulfilling five frequency-domain specifications simultaneously: phase margin ( ϕ m ), gain margin ( A m ), phase crossover frequency ( ω p c ), gain crossover frequency ( ω g c ) and a "flat phase" constraint. The control loop shape can be adjusted with wide freedom according to the five design specifications, which can all be beneficial on optimizing the control system: ω g c represents the system control bandwidth and response speed, ϕ m and A m guarantee the stability, and flat phase constraint keeps the system with iso-damping property on robustness of loop gain variations. The impact of ω p c adjustment is thoroughly discovered via frequency-domain analysis and also time-domain analysis with low-frequency disturbance and high-frequency noise. The frequency response functions are presented to show the loop-shaping advantages of the proposed synthesis scheme. A further in-depth study on designing guideline is also presented: the feasible region of four specifications, e.g. ω g c, ω p c, ϕ m and A m, can all be collected and visualized in the multi-dimensional graphics. This feasible region gives users prior information and great flexibility before the controller design. Simulation results using the designed FOPI λ D μ controller are carried out to demonstrate the performance advantages over the optimized integer-order PID, three-parameter FOPID, fractional filter-fractional order PID and Ziegler–Nichols FOPID controllers. Highlights: An FOPI λ D μ controller analytical design method for first order plus normalized time delay systems is proposed. The influence of phase crossover frequency on the loop-shaping of lower-frequency, higher-frequency bands and the resonance peak is clearly presented in this paper. A synthesis scheme to collect the comprehensive feasible regions of four frequency-domain specifications with the pseudo code is presented. Simulation results for a broad range of processes including lad-dominated, lag-delay balanced and delay-dominated ones demonstrated that the proposed FOPI λ D μ controller is applicable to a wide industrial use cases and outperforms the typical existing optimal controllers.